Input-Output Formalism for Few-Photon Transport: A Systematic Treatment Beyond Two Photons

TL;DR

This paper develops a systematic input-output formalism to analyze N-photon transport in waveguide systems, establishing a connection with Green functions and simplifying calculations, demonstrated through Kerr nonlinear cavity examples.

Contribution

It introduces a general framework linking N-photon S matrices with Green functions, simplifying computations via connectedness and effective Hamiltonians.

Findings

Derived a general connection between N-photon S matrix and Green functions.

Simplified N-photon transport calculations using connectedness and effective Hamiltonians.

Applied the formalism to compute up to 3-photon transport in a Kerr nonlinear cavity.

Abstract

We provide a systematic treatment of $N$-photon transport in a waveguide coupled to a local system, using the input-output formalism. The main result of the paper is a general connection between the $N$-photon S matrix and the Green functions of the local system. We also show that the computation can be significantly simplified, by exploiting the connectedness structure of both the S matrix and the Green function, and by computing the Green function using an effective Hamiltonian that involves only the degrees of freedom of the local system. We illustrate our formalism by computing $N$-photon transport through a cavity containing a medium with Kerr nonlinearity, with $N$ up to 3.